answer:
To solve the inequality -9 |-7n+9| - 5 ≤ 58, we can break it down into two cases based on the absolute value:
Case 1: (-7n+9) is positive or zero:
In this case, we can remove the absolute value symbols and rewrite the inequality as:
-9 (-7n+9) - 5 ≤ 58
Simplifying this, we get:
63n - 81 - 5 ≤ 58
63n - 86 ≤ 58
Adding 86 to both sides, we have:
63n ≤ 144
Dividing both sides by 63, we get:
n ≤ 144/63
Simplifying further, we have:
n ≤ 16/7 or n ≤ 2.2857
Case 2: (-7n+9) is negative:
In this case, we need to change the sign inside the absolute value and rewrite the inequality as:
-9 (-(-7n+9)) - 5 ≤ 58
Simplifying this, we get:
-9 (7n - 9) - 5 ≤ 58
-63n + 81 - 5 ≤ 58
-63n + 76 ≤ 58
Subtracting 76 from both sides, we have:
-63n ≤ -18
Dividing both sides by -63, we get:
n ≥ -18/-63 (Note: The inequality changes direction when dividing by a negative number.)
Simplifying further, we have:
n ≥ 2/7 or n ≥ 0.2857
Putting the solutions from both cases together, we have:
n ≤ 16/7 or n ≥ 2/7
Therefore, the solution to the given inequality is:
n ≤ 16/7 or n ≥ 2/7
Alli <3